One of the most powerful tests for a non-zero cosmological constant is
provided by a comparison of the expansion and oldest-star ages. To
quote
Carroll, Press and
Turner (1990),
``A high value of
H0 (> 80
km/s/Mpc, say), combined with no loss of confidence in a value 12-14
Gyr as a minimum age for some globular clusters, would
effectively prove the existence of a significant 
term. Given such observational results, we know of no convincing
alternative hypotheses.''
In Figure 3, the dimensionless product of
H0t0 is
plotted as a function of . Two
different cases are illustrated:
an open = 0 Universe, and a flat
Universe with
+ m = 1. Suppose that both
H0 and
t0 are both known to ± 10% (1-
, including
systematic errors). The dashed and dot-dashed lines indicate
1- and 2- limits, respectively for values of
H0 =
70 km/sec/Mpc and t0 = 15 Gyr. Since the two
quantities H0 and
t0 are completely independent, the two errors have
been added in
quadrature, yielding a total uncertainty on the product of
H_0t0 of ± 14% rms. These values of
H0 and t0
are consistent with a Universe where = 0.8,
m = 0.2. The
Einstein-de Sitter model (m = 1,
= 0) is excluded (at
2.5).
Despite the enormous progress recently in the measurements of
H0 and t0,
Figure 3 demonstrates
that significant further
improvements are still needed. First, in the opinion of this author,
total (including both statistical and systematic) uncertainties
of ± 10% have yet to be achieved for either H0 or
t0. Second, assuming that such accuracies will be
forthcoming in
the near future for H0 (as the Key Project, supernova
programs
and other surveys near completion), and for t0 (as
HIPPARCHOS
provides an improved calibration both for RR Lyraes and subdwarfs), it
is clear from this figure that if H0 is as high as 70
km/sec/Mpc, then accuracies of significantly better than ±
10% will be required to rule in or out a non-zero value for
. (If H0
were larger (or smaller), this discrimination would be simplified!)
|
Figure 3. The product of
H0t0 as a
function of |